论文标题
麦克斯韦幻影一般相对论
Maxwellian mirages in general relativity
论文作者
论文摘要
根据线性重力场中的自由度相对较新的结果，对麦克斯韦对线性一般相对性的近似值进行了重新审视。比较了在谐波坐标中获得的著名的麦克斯韦形式主义与在坐标选择下获得的麦克斯韦形式主义进行了比较，其中每个度量分量对应于线性重力场的每个坐标不变性自由度。可以利用一般相对性的坐标自由来将场方程投入到麦克斯韦形式，但这种形式仅仅是坐标选择的幻影 - 诸如矢量引力波之类的幻影。产生完美的Maxwellian场方程的坐标选择将产生不是Lorentzian的力方程。如果选择了字段定义以在力方程中获得类似Lorentz的术语，则在字段方程中损害了Maxwellian形式。引力 - 电磁作用的许多处理将使场方程和力方程之间的排序选择不一致，或者从力方程式截断了相关顺序的术语。这种错误通常反映了一种试图在场方程和力方程中同时强制麦克斯韦人类似物的尝试，结果掉落的术语与保留的术语一样大。
Maxwellian approximations to linear general relativity are revisited in light of relatively recent results on the degrees of freedom in the linear gravitational field. The well-known Maxwellian formalism obtained in harmonic coordinates is compared with a Maxwellian formalism obtained under a coordinate choice where each of the metric components corresponds to each of the coordinate-invariant degrees of freedom of the linear gravitational field. The coordinate freedom of general relativity can be exploited to cast the field equations into Maxwellian form, but such forms can be mere mirages of the coordinate choice -- mirages such as vector gravitational waves. A coordinate choice that yields perfectly-Maxwellian field equations, will yield a force equation that is not Lorentzian. If field definitions are chosen to obtain Lorentz-like terms in the force equation, then Maxwellian forms are compromised in the field equations. Many treatments of gravito-electromagnetism will make inconsistent ordering choices between the field equations and force equations, or else truncate terms of relevant order from the force equation. Often such mistakes reflect an attempt to force exact Maxwellian analogs simultaneously in both the field equations and the force equation, with the result that terms dropped are as large as those kept.
